Privault N. Understanding Markov Chains: Examples and Applications

2nd Edition . — Springer, 2018. — 379 p. — (Springer Undergraduate Mathematics Series). — ISBN: 9811306583.This book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes.Probability Background
Gambling Problems
Random Walks
Discrete-Time Markov Chains
First Step Analysis
Classification of States
Long-Run Behavior of Markov Chains
Branching Processes
Continuous-Time Markov Chains
Discrete-Time Martingales
Spatial Poisson Processes
Reliability Theory
Appendixes
Some Useful Identities
Solutions to Selected Exercises and Problems